Method and device for determining the relative position of two points

ABSTRACT

The invention relates to a method for determining the relative position of a mobile in relation to the known position of a reference station. The relative position calculation comprises the steps of: -a) choosing a linear combination of satellite transmission frequencies L 1  and L 2  from a predetermined list comprising at least two linear combinations of frequencies, -b) calculating a precise relative position Pp of the mobile in relation to the reference station on the basis of the linear combinations of pseudo-ranges corresponding to the linear combination and an estimated position Pe of the mobile in relation to the reference station, -c) choosing from the list the following linear combination, if it exists, and, in this case, reiterating step b), considering the estimated position to be said precise position Pp, -d) reiterating step c) for all the linear combinations in the list.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present Application is based on International Application No.PCT/FR03/00746, filed on Mar. 7, 2003, which in turn corresponds to FR02/02959 filed on Mar. 8, 2002, and priority is hereby claimed under 35USC §119 based on these applications. Each of these applications arehereby incorporated by reference in their entirety into the presentapplication.

The invention relates to the precise determination of the relativeposition of two points which may be several tens of kilometers apart, onthe basis of satellite positioning signals.

The field of application concerns the techniques requiring knowledge inthree-dimensions and with centimetric precision of the position of amobile in relation to the known position of a reference station at adistance of several tens of kilometers. Examples include geodesy,topography, hydrography, etc.

BACKGROUND OF THE INVENTION

In order to determine the relative position of a mobile in relation to areference station, satellite-based position-measuring means arecurrently used, employing, for example, radio signals transmitted by GPS(Global Positioning System) or other similar systems (GLONASS system,future GALILEO system) satellites.

In the GPS system, the signal transmitted by a satellite is coded andthe time taken by the signal to reach the point to be located is used todetermine the distance between this satellite and this point, preferablyreferred to as the pseudo-range to take account of synchronizationerrors between the satellite clock and the station clock. Thesesynchronization errors are conventionally eliminated through calculationwhen signals are received from at least four different satellites.Determination of the distance between the point to be located and aplurality of satellites, with knowledge of the geographic coordinates ofthe satellites, enables calculation of the coordinates of the point tobe located, most often coordinates expressed as latitude, longitude andaltitude at a fixed terrestrial reference point.

In order to determine the relative position of a mobile in relation to areference station, a method known as “differential GPS” is used, whichinvolves locating a point in relation to a reference station and not inrelation to an independent terrestrial reference point: by providing areceiver at the reference station, it is possible to determine therelative position of the mobile in relation to the reference stationusing measurements taken at the station and at the mobile.

The advantage of this method is that it enables to increase thepositioning precision. In fact, the measurement distortions linked tothe random characteristics of radio satellite signal propagation aremost often strongly correlated in space, and precise knowledge of theposition of the reference station allows these to be largely compensatedby comparing measurements taken at the station at theoretical distances.

Propagation time is determined on the one hand with reference to areference time of the pseudo-random code which modulates a carrierfrequency transmitted by the satellite, this code reference timeenabling in particular the approximate position of the mobile to bedetermined, i.e. accurate to within several meters to several tens ofmeters: the propagation time is determined on the other hand withreference to the phase of the received carrier, the phase measurement,which is less noisy than the code measurement, enabling the position ofthe mobile to be determined with greater precision, i.e. accurate towithin centimeters, but being dependent on elimination of the ambiguitysurrounding the number of phase rotations, since the phase can only beknown a priori to within 2π, where 2π corresponds to a distance equal tothe wavelength of the radio frequency signal transmitted by thesatellites.

Attention will be focused below on phase measurements only, since codeposition measurements can be performed in a conventional manner. Thepseudo-ranges supplied by the GPS receiver of the mobile or thereference station will therefore be considered essentially as numericalphase values, a phase value being directly converted into a distancevalue, with knowledge of the wavelength of the radio signal transmittedby the satellites.

The central point of centimetric positioning techniques using phasemeasurements is the preliminary calculation, referred to as“initialization”, in which the problem of ambiguities surrounding thenumber of wavelengths is resolved. This calculation conventionallyrequires prior knowledge of an estimated position of the mobile, whichmay be obtained in particular using a method such as that described inpatents FR 2 715 230 and FR 2 764 708. This estimated position is thenre-aligned with the precise position, then validated during thisinitialization calculation.

Particular consideration will then be given to the stage in which theestimated position is realigned towards a precise position.

The quality of this precise position depends in particular on thedistance between the mobile and the reference station.

In fact, flaws in the differential method initially arise due to thefact that radio satellite signals do not encounter exactly the samepropagation conditions on the satellite-station and satellite-mobilepaths. The differences in the conditions encountered, which are more orless zero in the immediate vicinity of the station, naturally increasewith distance.

This difference is mainly due to the ionosphere which is crossed bysatellite-station and satellite-mobile signals at different points,given that the ionosphere is not a homogeneous medium. The differentialmeasurements based on the propagation times of the satellite-station andsatellite-mobile signals are therefore adversely affected by thisdifference. This difference may result in an error in the position ofthe mobile in relation to the reference station ranging from 1 toseveral cm per km of distance. Thus, for a distance between the stationand the mobile which is greater than a distance in the order of 10 km,the position of the mobile in relation to the reference station cannotbe guaranteed with centimetric precision.

A first solution described in FR 2764708 A1 proposes, on the one hand,to reduce the initialization calculation time, in particular the timefor calculating an approximate unambiguous position using, inparticular, linear combinations of transmission frequencies L1 and L2 ofGPS system satellites. On the other hand, it proposes to reduce theionospheric error; the reduction in the ionospheric error applies duringthe realignment phase. It consists in calculating, on the basis of theapproximate unambiguous position, on the one hand, a position (XL1, YL1,ZL1) for L1 and, on the other hand, a position (XL2, YL2, ZL2) for L2,the precise position (X, Y, Z) then resulting from the following linearcombination: X=(1.65 XL1−XL2)/0.65 Y=(1.65 YL1−YL2)/0.65 Z=(1.65ZL1−ZL2)/0.65.

However, due to the calculation of a position on L1, adversely affectedby an ionospheric error E, and the calculation of the position on L2,adversely affected by an ionospheric error 1.65*E, it is still notpossible to eliminate ambiguities if the ionospheric error increases,which occurs when the distance between the mobile and the referencestation increases.

A different solution conventionally proposed consists in providing notone but a plurality of reference stations, constituting what is commonlyreferred to as a “network”. According to this technique, it is possibleto know not only the errors measured at one point, as is done in thecase of “differential GPS”, but also their gradient of evolution in thezone. The effect of spatial decorrelations of the errors is thereforelargely compensated. This solution is effective, but is of courselaborious and costly to implement due to the infrastructure which itrequires and the cost of the communications between the stations and themobile. Furthermore, such an infrastructure will not exist everywhere.

A method based on exploitation of the fact that the ionospheric error isa function of frequency (1/f² in the first approximation) has also beenproposed.

It is then possible to determine this error or to reduce or eveneliminate it by replacing the frequency f (designated by L1 or L2 in thecase of the GPS system) in the calculations with a linear combination ofthe carrier frequencies of the signals transmitted by the satellites,i.e. by a linear combination of L1 and L2.

The result of a linear combination of L1, L2 is a new frequency L3 towhich a wavelength referred to as the apparent wavelength corresponds.

For example, in the case of the GPS system in which L1=1.57542 GHz(corresponding to a wavelength of around 19 cm) and L2=1.22760 GHz(corresponding to a wavelength of around 24 cm), the combination offrequencies referred to as “Iono-Free”, 9L1−7L2 allows the ionosphericerror to be almost completely eliminated. The corresponding apparentwavelength is 5 cm.

However, this method is very difficult to apply due to the greatdifficulty in eliminating the ambiguities surrounding such shortwavelengths.

SUMMARY OF THE INVENTION

The object of the invention is therefore to propose a method and adevice which enables the position of a mobile in relation to a referencestation, possibly at a distance of several tens of kilometers, to beobtained with centimetric position.

To achieve this object, the invention proposes a method for determiningthe relative position of a mobile in relation to the known position of areference station, each using an antenna for receiving radio signalsoriginating from an arrangement of positioning satellites transmittingon at least two frequencies L1 and L2, this method comprising theperiodic determination, for each of said frequencies, of a set of 2ppseudo-ranges, i.e. p pseudo-ranges between the mobile and the psatellites and p pseudo-ranges between the reference station and the psatellites, the supply of the pseudo-ranges to a position-calculatingunit, and the calculation by this unit of a relative position of themobile in relation to the reference station based, on the one hand, onthe pseudo-ranges and, on the other hand, on an estimated position Pe ofthe mobile in relation to the reference station, this method beingmainly characterized in that, for a given set of 4p pseudo-rangesreceived by the calculating unit, the calculation of the relativeposition comprises the following steps which consist in:

-   -   a) choosing a linear combination aL1+bL2 of said frequencies L1        and L2 from a predetermined list comprising at least two linear        combinations of frequencies,    -   b) calculating the linear combinations of pseudo-ranges        corresponding to said linear combination, and, on the basis of        these linear combinations of pseudo-ranges and the estimated        position Pe, calculating a precise relative position Pp of the        mobile in relation to the reference station,    -   c) choosing from the list the following linear combination, if        it exists, and, in this case, reiterating step b), considering        the estimated position to be said precise position Pp, and using        the same set of 4p pseudo-ranges to obtain an even more precise        relative position,    -   d) reiterating step c) for all the linear combinations in the        list.

A plurality of calculations of the position of the mobile are thussuccessively carried out on the basis of the same set of measurements ofthe pseudo-ranges using different linear combinations of frequencies,the estimated position at the beginning of a calculation being theposition calculated in the preceding step.

In the preceding technique, a single calculation was carried out and thelinear combination used in this calculation was related to the positionsrespectively calculated for each of the frequencies L1 and L2.

An important characteristic of the invention is that the linearcombinations in the list are determined in such a way that thecorresponding wavelengths reduce progressively and the sensitivity toionospheric errors also reduces progressively and more rapidly than thewavelength.

In other words, the first linear combination of frequencies is chosen sothat its wavelength is long in order to facilitate the elimination ofambiguity surrounding the number of phase rotations; but, conversely,this first linear combination may correspond to a significantsensitivity to ionospheric errors. Since the estimated position Pe hasbeen improved following this first realignment, the second linearcombination in the list corresponds to a shorter wavelength and to evenless ionospheric error. This process continues, using shorter andshorter wavelengths and lower and lower sensitivities to ionosphericerrors.

In the context of the GPS system, the first combination may be thecombination L1−L2 (a=1, b=−1); the last may be 9L1−7L2 (a=9, b=−7), acombination known to be virtually immune to ionospheric errors.

The intermediate combinations are preferably as follows (in sequence):2L1−L2; 3L1−2L2; 4L2−3L1.

According to a different characteristic aspect of the invention, step b)of the calculation is carried out either in a single step directly usingthe p satellites, or in two steps, the first of which uses only areduced number p′ (p′<p) of satellites and the second uses the psatellites. It is preferably only on using the first linear combination(longest wavelength) that the calculation is made in two steps, theother linear combinations being used according to a calculation in asingle step with the p satellites.

If step b) is carried out in two steps, it advantageously corresponds tothe following steps, consisting in:

b1) calculating an approximate relative position Pa of the mobile inrelation to the reference station on the basis of the chosen linearcombination, Pe and a subset of 4p′ pseudo-ranges corresponding to p′satellites, where p′ is less than p and where the p′ satellites chosenfrom the arrangement of p satellites are those which, taking intoaccount the current geometry of the arrangement, are least sensitive toan error in the estimated position.

b2) calculating a precise relative position Pp of the mobile in relationto the reference station on the basis of said linear combination, Pa andthe complete set of 4p pseudo-ranges.

According to a different characteristic of the invention, the 2ppseudo-ranges between the satellites and the reference station aredetermined by the reference station and sent by radio to the mobilewhich then comprises reception means for receiving these pseudo-rangesand information for dating the measurement of these pseudo-ranges.

Finally, the object of the invention is not only the method fordetermining the relative position of a mobile in relation to the knownposition of a reference station, the general outline of which has justbeen described, but also a device for determining the position of amobile in relation to a reference station capable of carrying out thismethod. The device according to the invention comprises at least, in themobile, means for receiving satellite positioning signals and means forreceiving a set of 2p pseudo-ranges transmitted by the reference stationand representing the pseudo-ranges between the reference station and psatellites for at least two different carrier frequencies L1 and L2,means for periodic determination of a set of 2p pseudo-ranges betweenthe mobile and the p satellites, means for supplying the 4ppseudo-ranges to a position-calculating unit, means for storing a listof linear combinations of the frequencies of the positioning signalcarriers, means for carrying out, on the basis of the same set of 4ppseudo-ranges, successive calculations of the relative position of themobile in relation to the position of the reference station, each timebased on a different linear combination of frequencies chosen from thelist, an estimated position Pe and the set of 4p pseudo-distances, theposition estimated in a calculation with a given linear combination fromthe list being the relative position calculated on the basis of thepreceding linear combination from the list.

Still other objects and advantages of the present invention will becomereadily apparent to those skilled in the art from the following detaileddescription, wherein the preferred embodiments of the invention areshown and described, simply by way of illustration of the best modecontemplated of carrying out the invention. As will be realized, theinvention is capable of other and different embodiments, and its severaldetails are capable of modifications in various obvious respects, allwithout departing from the invention. Accordingly, the drawings anddescription thereof are to be regarded as illustrative in nature, andnot as restrictive.

BRIEF DESCRIPTION OF THE DRAWINGS

Other characteristics and advantages of the invention will be explainedin the detailed description which follows, provided as a non-limitingexample, with reference to the attached drawings, in which:

FIG. 1 schematically shows a distribution of the positions of thereference station, the mobile, and the estimated, approximate andprecise positions of the mobile in relation to the position of thereference station;

FIG. 2 schematically shows the device according to the invention;

FIG. 3 shows a flow diagram of the calculations performed.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 shows the position R of the reference station at a distance D,which may be several tens of kilometers, from a mobile whose trueposition is M. This figure also shows the estimated position Pe,approximate position Pa, and precise position Pp of the mobile whichwill be referred to later. The point Pe corresponds to the position M ofthe mobile estimated to within several meters (1 to 2 meters, forexample), the point Pa corresponds to that of the mobile calculated withan error of one to several decimeters, the point Pp corresponds to thatof the mobile calculated with a maximum error of several centimeters.

The reference station and the mobile are equipped with an antenna 10 and12 respectively for receiving radio signals originating from positioningsatellites (GPS or other system) and means for demodulating andprocessing the received signals. The mobile periodically calculatespseudo-ranges between its position and the position of the satellites ata given time. The station calculates pseudo-ranges in the same manner(measured at the same time, or reduced to the same measuring time)between its position on the position of the satellites. As already seenin the preamble, the pseudo-ranges are conventionally supplied in theform of a first numerical value which defines the temporal position ofthe pseudo-random code transmitted by a satellite at a given time, and asecond numerical value which defines the phase of the radio frequencysignal modulated by this code at the same time.

In simple, low-precision receivers (mobiles or reference stations), asingle coded radio frequency signal is used by the receiver circuits. Inmore precise receivers, on which the present invention focuses, at leasttwo signals with a different carrier frequency, L1 and L2 originatingfrom the satellites, are processed by the receiver. The receivertherefore periodically calculates the pseudo-ranges for each of thefrequencies L1 and L2.

As a result, for a position measurement at a given time based on psatellites, the position calculation will involve a set of 4ppseudo-ranges, therefore 4p phase measurements, which are respectively:

-   -   p phase measurements between the reference station and the p        satellites, at the frequency L1,    -   p phase measurements between the mobile and the p satellites,        again at the frequency L1,    -   p phase measurements between the reference station and the p        satellites, at the frequency L2,    -   and p phase measurements between the mobile and the p        satellites, at the frequency L2.

The reference station is equipped with means for transmitting thenumerical values which it has determined to the mobile. The mobile isequipped with means for receiving them (antenna 11 in FIG. 2), so that,for a position calculation at a given time, the mobile has not only itsown measurements of pseudo-ranges, but also measurements ofpseudo-ranges determined by the reference station.

In the mobile, the signals originating from the reference station andthe signals received directly by the mobile are used by an electronicassembly 14 which the mobile comprises, as shown in FIG. 2. However, theinverse solution could be envisaged, wherein the calculations are madeby the reference station, the mobile transmitting the pseudo-rangeswhich it has calculated to the latter. In this method, the location ofthe mobile is known to the station at all times, which may be useful incertain applications.

This electronic assembly 14 first comprises a satellite positioningreceive circuit 16 capable of determining measurements of thepseudo-ranges between its antenna and a plurality of satellites.

The receive circuit 16 periodically (for example every 100 milliseconds)supplies a set of 2p pseudo-ranges when p satellites are in directline-of-sight with the antenna 12. It transmits them to a relativeposition calculating unit 18 which furthermore receives the set of 2ppseudo-ranges corresponding to the 2p pseudo-ranges received from thesame p satellites by the antenna 10 of the reference station andtransmitted to the mobile by the antenna 11.

The function of the relative position calculating unit 18 is todetermine the precise position Pp of the antenna 12 of the mobile inrelation to the antenna 10 of the reference station.

The calculating unit 18 is programmed to carry out the requiredcalculations and is connected to the peripheral units required accordingto the applications: display 20, keyboard 22, data or programreader/recorder 24, means for wired or radio transmission to a user, orsimple interface to output the result of the calculations to atransmission line.

The calculating means provided in the calculating unit are suitable forcarrying out the operations described below, on the basis of the set of4p pseudo-ranges received and a given time by the mobile.

The position calculation is differential, i.e. the position of themobile is determined in relation to the reference station (thecalculation being carried out by either the mobile or the station).Therefore, the position calculation can then be considered to consist incalculating the position of the mobile on the basis of differentialmeasurements of pseudo-ranges, producing differences betweenpseudo-ranges measured at the reference station and at the mobile. Thecalculation involves a notion of double differences of pseudo-ranges(differences between pairs of satellites) which will be described below.

Globally, using the conventional notion of double difference, thedifferential calculation principle is as follows:

-   -   the positions of the satellites are calculated at the        measurement time t, using the ephemerides of the satellites;    -   the differential differences between the reference station and        the mobile are determined on the basis of the differential        measurements of pseudo-ranges, according to the boresight axes        of the satellites. Distances are obtained which can be globally        considered as the projections, along these axes, of the distance        D between the mobile and the reference station; these are        measured distances;    -   the distances along the same axes between the reference station        and an estimated position Pe of the mobile are calculated for        the same measurement time; these are estimated distances;    -   the difference between the measured distance and the estimated        distance is determined according to each axis, and can be        referred to as the extent of deviation or “innovation” according        to this axis;    -   the deviations between the measured position of the mobile and        the estimated position are calculated on the basis of these        extents of deviation, using the director cosines representing        the directions of the boresight axes of the satellites;    -   the calculated deviations are added to the estimated position to        produce a calculated position of the mobile which is either a        final position Pp or a new estimated position Pe intended for a        subsequent calculation step which will be described below.

As will be explained below, the double differences considered in thepresent invention are obtained, not on the basis of directly measuredfrequencies, but on the basis of linear combinations of thepseudo-ranges measured at the frequency L1 and the pseudo-rangesmeasured at the frequency L2.

An essential element of the present invention resides in the fact that aplurality of calculations of the position of the mobile are carried outsuccessively on the basis of the same set of 4p measurements ofpseudo-ranges using different linear combinations of the phasescorresponding to the frequencies L1 and L2. This entails a calculationof the theoretical phases of a carrier frequency which wouldtheoretically be the linear combination of the frequencies L1 and L2. Aplurality of linear combinations are successively used for the same setof 4p pseudo-ranges; the calculation uses the pseudo-ranges and anestimated position, and arrives at a position calculated for a givenlinear combination; the position calculated for this linear combinationserves as the estimated position for a subsequent calculation using adifferent linear combination. The succession of linear combinations,corresponding to different apparent wavelengths, is such that theprecision of the calculation increases progressively. The linearcombinations of frequencies are chosen from one calculation to the nextin particular in such a way that the corresponding apparent halfwavelength is equal to or greater than the position error resulting fromthe preceding calculation, while reducing ionospheric error.

As shown below, double differences established for pairs of satellites,determined in such a way as to further increase the apparent wavelength,taking into account the geometry of the arrangement of satellites (theapparent wavelength of a pair of satellites is longer when viewed from anarrow angle), are used in the position calculations.

By judiciously combining the choice of linear combinations offrequencies and pairs of satellites, it is therefore possible toprogress from an estimated position of decimetric or even metricprecision to the desired position of centimetric precision. The linearcombinations are chosen from a list, an example of which is given below.This list is stored, for example, in the unit 24 to be used by thecalculating unit 18.

In the case of GPS, the linear combinations apply to the frequencies L1and L2. The result of a linear combination of L1, L2 is a new frequencyL3 to which a wavelength referred to as the apparent wavelengthcorresponds. The receive circuit 16 supplies the calculating unit 18with the phase φ_(L1) of the signal transmitted by the satellite for L1and the phase φ_(L2) of the signal transmitted by the satellite for L2,these two phases representing the distance between the satellite and themobile; the calculating unit 18 will then be able to use, not the phaseφ_(L1) or the phase φ_(L2), but a phase φ_(L3) corresponding to thefollowing linear combination:L3=a.L1+b.L2 according to the formula φ_(L3) =a.φ _(L1) +b.φ _(L2)

Similarly, the reference station sends phases to the mobile,representing, for each satellite, the distance between the satellite andthe reference station, and the same linear combination can be used todetermine an apparent phase at the wavelength L3.

The numbers a and b are the coefficients of the chosen linearcombination.

For each linear combination, not only the apparent wavelength (andtherefore the distance beyond which the phase measurement becomesambiguous), but also the sensitivity to ionospheric propagation errorscan be calculated. If the error existing at the frequency L1 is taken asthe reference ionospheric error value, the corresponding error value foreach linear combination can be calculated. If, for example, the error onL1 is 1 cm/km of distance, the error on L1 for a distance of 10 km toseveral tens of kilometers would reach 10 cm to several tens of cm.

To correct this error, direct use of a linear combination of frequenciescould be envisaged, producing very low ionospheric propagation error;the combination referred to as “Iono-Free” 9L1−7L2 has very littleerror; but it corresponds to a very short apparent wavelength (5 cm) sothat it is impossible to eliminate its phase ambiguity on the basis of adistant estimated position.

For GPS and as a preferred example, the following ordered list of linearcombinations has been drawn up with the corresponding apparentwavelength and the ionospheric error coefficient (relative to the unitreference value for the frequency L1). The apparent wavelengths aredecreasing, and the ionospheric error coefficients decrease even morerapidly.

L1−L2, known to the person skilled in the art by the name of“Wide-Lane”, which corresponds to an apparent wavelength of around 86 cmwith an ionospheric error ratio in relation to the basic frequency L1 of1.3;

2L1−L2, which corresponds to an apparent wavelength of around 16 cm withan ionospheric error ratio in relation to the basic frequency L1 of0.56;

3L1−2L2, which corresponds to an apparent wavelength of around 13 cmwith an ionospheric error ratio in relation to the basic frequency L1 of0.3;

4L2−3L1, which corresponds to an apparent wavelength of around 11 cmwith an ionospheric error ratio in relation to the basic frequency L1 of0.1;

9L1−7L2 which, as already mentioned, is known as “Iono-Free”,corresponding to an apparent wavelength of around 5 cm with anionospheric error ratio in relation to the basic frequency L1 close tozero.

This sequence of linear combinations is of course only one example,adapted to GPS in its current situation: it will differ in particular inthe case of frequencies L1 and L2 which differ from those specified(future developments of GPS, other radio satellite systems such asGalileo); it may also contain only some of these linear combinationsand/or may incorporate others.

The principle is that, with a set of 4p pseudo-ranges combined in linearfashion, the calculation can be carried out using an estimated positionand the first linear combination from the list, with a low risk of phaseambiguity due to the long wavelength of this combination; a firstcalculated position is obtained which is more precise than the estimatedposition. This calculated position serves as an estimated position for adifferent calculation carried out with the same 4p pseudo-ranges, butcombined according to the following combination from the list,corresponding to an apparent wavelength which is shorter, but still longenough so as not to introduce phase ambiguity, taking into account theionospheric error prevailing following the first calculation. A new,even more precise, calculated position is achieved. This more preciseposition serves as an estimated position for a third calculation withthe same set of pseudo-ranges, combined according to the third linearcombination from the list, and so on. With each step, the position isimproved due to the reduction in the ionospheric error, and theimprovement in this position enables the choice, in the following step,and without risk of the ambiguity error, of a shorter wavelength which,with an even greater reduction in the ionospheric error, allows thecalculated position to approximate more closely the true position.

FIG. 3 schematically shows the main steps of the calculations carriedout.

A set of 4p pseudo-ranges is supplied to the calculating unit (step 1)which furthermore determined an estimated position Pe and which choosesthe first linear combination of frequencies from the predetermined list(step 2).

Optionally, the calculation of a position on the basis of an estimatedposition and a given linear combination may be carried out in two mainsteps:

-   -   an approximate position Pa is calculated on the basis of the        estimated position Pe of the chosen linear combination of        frequencies and a set of 4p′ pseudo-ranges (step 3 a).    -   a precise position Pp is then calculated on the basis of the        approximate point Pa, the same chosen linear combination of        frequencies and the complete set of 4p pseudo-ranges (step 3 b).

In a variant of the invention, it is possible to calculate directly inone step the precise position Pp on the basis of the estimated positionPe, the chosen linear combination of frequencies and a complete set of4p pseudo-ranges; the calculation may be carried out, for example, intwo steps for the first linear combination, and in one step for thefollowing linear combinations.

If all the linear combinations from the list have not yet been used(step 4), the following linear combination is chosen from the list andsteps 3 a and 3 b are reiterated, taking the calculated position Ppresulting from step 3 b as the estimated position (step 5).

If all the linear combinations from the list have been used, theposition Pp resulting from the last calculation is validated (step 6) byconventionally determining the coherence value of the calculatedposition, to reject the solutions which do not satisfy minimum coherencecriteria. At the end of this validation step, the position Pp is theposition of the mobile, established with centimetric precision.

If the position Pp is not validated, the steps described are carried outon the basis of a different set of 4p pseudo-ranges.

Details will now be provided, as an example, of the calculation of steps3 a and 3 b which can be carried out to obtain a precise position Ppfrom an estimated position Pe.

The phase in which an approximate position Pa (step 3 a) is obtaineduses an initial estimated position Pe; and it advantageously uses asub-set of 4p′ pseudo-ranges chosen from the set of 4p pseudo-ranges.

The position calculation is carried out by double-difference processingof the 4p′ pseudo-ranges.

The processing known as “double-difference” consists in working, notdirectly on the basis of the differences for two satellites betweenpseudo-ranges, but on the basis of differences between the referencestation and the mobile, of the difference for two satellites betweenpseudo-ranges.

These pairs of satellites are chosen according to their sensitivity toposition errors, this sensitivity been dependent on the geometry betweenthe satellites and the measurement point. Since the geometry ofvisibility of the p satellites at the measurement time is known thanksto the ephemerides and the estimated position, the pairs of satellitescan be classified in the order of their increasing sensitivity toposition errors. Only the p′ satellites corresponding to the leastsensitive pairs will be used, allowing the apparent wavelength to beincreased. More precisely, the double differences of the following typewill be calculated:DDij=(Dim−Djm)−(Dir−Djr), in which:

Dim is the pseudo-range from the mobile to the satellite in row i,

Djm is the pseudo-range from the mobile to the satellite in row j,

Dir is the pseudo-range from the reference station to the satellite inrow i,

Djr is the pseudo-range from the reference station to the satellite inrow j.

Differences of the Dim−Djm or Dir−Djr type allow the errors common tothe satellites (clock differences between the satellites and thereceiver) to be eliminated.

The differences between these differences, or double differences DDij,allow the errors due to atmospheric or ionospheric propagation to beeliminated.

The double differences are calculated on the one hand for the frequencyL1 (difference DDij1) and, on the other hand for the frequency L2(difference DDij2). A linear combination of double differencesCLij=aDDij1+bDDij2 is then calculated for a first linear combination offrequencies L3=aL1+bL2. These are the linear combinations which will beused, rather than the conventional double differences, for the positioncalculation; they represent a phase at the apparent wavelength of thefictitious frequency L3 and are expressed here as distances.

The combinations of double differences CLij are compared to similarcombinations, calculated and not measured, on the basis of the initialestimated position Pe. The difference resulting from this comparison isreferred to as INNOVij, representing the deviation between theestimation and the measurement.

These deviations are linked to the deviations of longitude, latitude andaltitude DL, DG and DA between the estimated position (here the initialposition Pe) and the calculated position (here the approximatecalculated position Pa) by equations of the typeINNOVij=DL[cos(Evi)cos(Azi)−cos(Evj)cos(Azj)]+DG[cos(Evi)sin(Azi)−cos(Evj)sin(Azj)]+DA[sin(Evi)−sin(Evj)]

where Evi, Evj are the elevations of the satellites i and j, and Azi,Azj are their azimuths.

A simple calculation, or matrix calculation with minimization of errorsusing the least squares technique if there are more than 4 satellites,allows DL, DG, DA to be determined, representing deviations between themeasured position and the estimated position. These deviations are addedto the longitude, latitude, and altitude of the estimated position Pe toobtain an approximate position Pa.

A second calculation step (step 3 b) is carried out on the basis of thisapproximate position Pa. The second step is very similar to the first,but

-   -   it uses all the 4p pseudo-ranges, i.e. those corresponding to        all the satellite pairs,    -   it uses the approximate position Pa rather than the initial        estimated position Pe as the estimated position,    -   it uses a matrix calculation with a number of equations which is        generally higher than the number of unknowns (the number p of        satellites being assumed to be greater than 4) for calculating a        precise position Pp; the deviations DL, DG, DA between the        estimated position and the calculated position can then be        conventionally determined using a least squares method (the        position determined by calculation is the position which        minimizes the mean square value of the residues).

The position Pp is then used in a new calculation as the estimatedposition, instead of the position Pe, using the following linearcombination from the list.

Progressively, by iteration through to the end of the list, anincreasingly precise and unambiguous value of the position of the mobileis obtained.

It will be readily seen by one of ordinary skill in the art that thepresent invention fulfills all of the objects set forth above. Afterreading the foregoing specification, one of ordinary skill will be ableto affect various changes, substitutions of equivalents and variousother aspects of the invention as broadly disclosed herein. It istherefore intended that the protection granted hereon be limited only bythe definition contained in the appended claims and equivalents thereof.

1. A method of determining the relative position of a mobile in relationto the known position of a reference station, each using an antenna forreceiving radio signals originating from an arrangement of positioningsatellites transmitting on at least two frequencies L1 and L2, thismethod comprising the steps of: periodically determining, for each ofsaid frequencies, of a set of 2p pseudo-ranges, for p pseudo-rangesbetween the mobile and the p satellites and p pseudo-ranges between thereference station and the p satellites, supplying of the pseudo-rangesto a position-calculating unit, and calculating by theposition-calculating unit of a relative position of the mobile inrelation to the reference station based on the pseudo-ranges and on anestimated position Pe of the mobile in relation to the referencestation, and, for a given set of 4p pseudo-ranges received by theposition-calculating unit, calculating the relative position, comprisingthe following steps: a) choosing a linear combination equation aL1+bL2of said frequencies L1 and L2 from a predetermined list having at leasttwo linear combination equations of frequencies, b) calculating linearcombinations of pseudo-ranges corresponding to the chosen linearcombination equation, and, on the basis of these linear combinations ofpseudo-ranges and the estimated position Pe, calculating a preciserelative position Pp of the mobile in relation to the reference station,c) choosing from the list the following linear combination equation,setting the estimated position Pe to be a new estimated position Peequal to said precise position Pp, and reiterating steps b) bycalculating new linear combination equation using the same set of 4ppseudo-ranges and, on the basis of the new linear combination ofpseudo-ranges and the new estimated position Pe, obtaining an even moreprecise relative position, d) reiterating step c) for all the remaininglinear combination equations in the list.
 2. The method according toclaim 1, wherein the linear combination equations in the list aredetermined in such a way that, from one calculation to the next, thecorresponding wavelengths reduce progressively and the sensitivity toionospheric errors also reduces progressively.
 3. The method accordingto claim 2, wherein the first combination equation in the list is thecombination equation L1−L2 (a=1, b=−1) and/or the last linearcombination equation in the list is the combination equation 9L1−7L2(a=9, b=−7), L1 and L2 being the transmission frequencies of thesatellites of the GPS system.
 4. The method according to claim 2,wherein the intermediate combination equations are as follows: 2L1−L2(a=2, b=−1); 3L1−2L2 (a=3, b=−2); 4L2−3L1 (a=4, b=3).
 5. The methodaccording to preceding claim 2, wherein step b) comprises the followingtwo steps: b1) calculating an approximate relative position Pa of themobile in relation to the reference station on the basis of the chosenlinear combination equation, Pe and a subset of 4p′ pseudo-rangescorresponding to p′ satellites, where p′ is less than p and where the p′satellites chosen from the arrangement of p satellites are those which,taking into account the current geometry of the arrangement, are leastsensitive to an error in the estimated position, b2) calculating aprecise relative position Pp of the mobile in relation to the referencestation on the basis of said linear combination of Pa and the completeset of 4p pseudo-ranges.
 6. The method according to claim 2, wherein thesteps b1) and b2) are only carried out for the first linear combinationequation in the list, a single step involving the 4p pseudo-ranges beingcarried out for the other linear combination equations in the list. 7.The method according to claim 2, wherein the 2p pseudo-ranges betweenthe satellites and the reference station are determined by the referencestation and sent by radio to the mobile which then comprises receptionmeans to receive these pseudo-ranges and information for dating themeasurement of these pseudo-ranges.
 8. The method according to claim 1,wherein the first combination equation in the list is the combinationequation L1−L2 (a=1, b=−1) and/or the last linear combination equationin the list is the combination equation 9L1−7L2 (a=9, b=−7), L1 and L2being the transmission frequencies of the satellites of the GPS system.9. The method according to claim 8, wherein the intermediate combinationequations are as follows: 2L1−L2 (a=2, b=−1); 3L1−2L2 (a=3, b=−2);4L2−3L1 (a=4, b=−3).
 10. The method according to preceding claim 8,wherein step b) comprises the following two steps: b1) calculating anapproximate relative position Pa of the mobile in relation to thereference station on the basis of the chosen linear combinationequation, Pe and a subset of 4p′ pseudo-ranges corresponding to p′satellites, where p′ is less than p and where the p′ satellites chosenfrom the arrangement of p satellites are those which, taking intoaccount the current geometry of the arrangement, are least sensitive toan error in the estimated position, b2) calculating a precise relativeposition Pp of the mobile in relation to the reference station on thebasis of said linear combination of Pa and the complete set of 4ppseudo-ranges.
 11. The method according to claim 8, wherein the stepsb1) and b2) are only carried out for the first linear combinationequation in the list, a single step involving the 4p pseudo-ranges beingcarried out for the other linear combination equations in the list. 12.The method according to claim 8, wherein the 2p pseudo-ranges betweenthe satellites and the reference station are determined by the referencestation and sent by radio to the mobile which then comprises receptionmeans to receive these pseudo-ranges and information for dating themeasurement of these pseudo-ranges.
 13. The method according to claim 1,wherein the intermediate combination equations are as follows: 2L1−L2(a=2, b=−1); 3L1−2L2 (a=3, b=−2); 4L2−3L1 (a=4, b=−3).
 14. The methodaccording to preceding claim 13, wherein step b) comprises the followingtwo steps: b1) calculating an approximate relative position Pa of themobile in relation to the reference station on the basis of the chosenlinear combination equation, Pe and a subset of 4p′ pseudo-rangescorresponding to p′ satellites, where p′ is less than p and where the p′satellites chosen from the arrangement of p satellites are those which,taking into account the current geometry of the arrangement, are leastsensitive to an error in the estimated position, b2) calculating aprecise relative position Pp of the mobile in relation to the referencestation on the basis of said linear combination of Pa and the completeset of 4p pseudo-ranges.
 15. The method according to claim 13, whereinthe steps b1) and b2) are only carried out for the first linearcombination equation in the list, a single step involving the 4ppseudo-ranges being carried out for the other linear combinationequations in the list.
 16. The method according to preceding claim 1,wherein step b) comprises the following two steps: b1) calculating anapproximate relative position Pa of the mobile in relation to thereference station on the basis of the chosen linear combinationequation, Pe and a subset of 4p′ pseudo-ranges corresponding to p′satellites, where p′ is less than p and where the p′ satellites chosenfrom the arrangement of p satellites are those which, taking intoaccount the current geometry of the arrangement, are least sensitive toan error in the estimated position, b2) calculating a precise relativeposition Pp of the mobile in relation to the reference station on thebasis of said linear combination of Pa and the complete set of 4ppseudo-ranges.
 17. The method according to claim 16, wherein the stepsb1) and b2) are only carried out for the first linear combinationequation in the list, a single step involving the 4p pseudo-ranges beingcarried out for the other linear combination equations in the list. 18.The method according to claim 1, wherein the steps b1) and b2) are onlycarried out for the first linear combination equations in the list, asingle step involving the 4p pseudo-ranges being carried out for theother linear combination equations in the list.
 19. The method accordingto claim 1, wherein the 2p pseudo-ranges between the satellites and thereference station are determined by the reference station and sent byradio to the mobile which then comprises reception means to receivethese pseudo-ranges and information for dating the measurement of thesepseudo-ranges.
 20. A device for determining the position of a mobile inrelation to a reference station, comprising: means for receivingsatellite positioning signals; means for receiving a set of 2ppseudo-ranges transmitted by the reference station and representing thepseudo-ranges between the reference station and p satellites for twodifferent carrier frequencies L1 and L2, means for periodicdetermination of a set of 2p pseudo-ranges between the mobile and the psatellites, means for supplying the 4p pseudo-ranges to aposition-calculating unit, means for storing a list of linearcombination equations of the frequencies of the positioning signalcarriers, and means for carrying out, on the basis of the same set of 4ppseudo-ranges, successive calculations of the relative position of themobile in relation to the position of the reference station, each timebased on a different linear combination equation of frequencies chosenfrom the list, an estimated position Pe and the set of 4p pseudo-ranges,and when the chosen linear combination equation is different from thefirst linear combination equation in the list, the estimated position Pebeing set as the relative position calculated in the precedingsuccessive calculation on the basis of the preceding linear combinationequation from the list.